Final answer:
To find the diameter of the moon's image produced by a telescope lens, we use the relationship between the focal length of the lens, the actual diameter of the moon, and the Earth-Moon distance. By setting up a ratio of these values, we can solve for the image diameter.
Step-by-step explanation:
The question asks to find the diameter of the moon's image when viewed through a telescope with an objective lens of focal length 1.26 meters. To find the image diameter, we will use the lens formula and the concept of similar triangles, as the image produced by the lens is similar in shape to the actual object but scaled according to the ratio of the focal length to the actual object distance.
We can find the image size using the formula:
Image diameter / Moon diameter = Focal length / Earth-Moon distance
Plugging in the given values:
Image diameter / 3.48 × 106 m = 1.26 m / 3.84 × 108 m
Solving for the image diameter yields a value that enables us to understand the magnification power of the telescope's lens for the moon observation.